FIG. 1 illustrates the traditional way of sample rate conversion as a separate block in an Analog to Digital Converter (ADC). Specific digital sampling frequencies are indicated via f1 and f2. Analog input 110 may be input to discrete-time analog Delta-Sigma ADC 120, outputting digital data at a first sampling frequency f1. Digital low-pass filter 130 may remove unwanted components from the digital data, which is then sent to a sample rate converter 140, which outputs the digital data at a second (desired) sampling frequency f2. As illustrated in FIG. 1, this Prior Art approach requires separate components for the sample rate conversion and also for the ADC. Moreover, traditional sample-rate conversion techniques can be cumbersome and difficult to implement.
Frequency domain effects of sample rate conversion can be analyzed by upsampling the original digital samples by an integer M, and then downsampling that sequence by N. For example, if f2=0.8f1, then upsampling by M=4 and then downsampling by N=5 gives the desired sample rate transformation. FIGS. 3-7 illustrate the process in the frequency domain. (The dots indicate that the images are repeated, but only the ones of interest are illustrated.)
FIG. 3 shows the repeated images of the original spectrum sampled at f1, when it is upsampled by 4. FIG. 4 divides the upsampled spectrum into 5 equal pieces in preparation for downsampling by 5. The dotted lines indicate the boundaries of the 5 equal pieces, and the line marked N=5 corresponds to the new sampling frequency f2. FIG. 5 shows images, which must be removed via filtering prior to downsampling, and the dash-dot line corresponds to the magnitude response of the filter used to remove the images. FIG. 6 shows the results after the filter removes the images. FIG. 7 shows the new spectrum with sampling rate f2.
Thus, in a traditional design, such as illustrated in FIG. 1, a low-pass filter is required to remove the quantization noise produced by the delta-sigma ADC, and another filter may also be required to remove images as part of the sample rate conversion.